Spectral: Solving Schroedinger and Wheeler-DeWitt equations in the positive semi-axis by the spectral method

The Galerkin spectral method can be used for approximate calculation of eigenvalues and eigenfunctions of unidimensional Schroedinger-like equations such as the Wheeler-DeWitt equation. The criteria most commonly employed for checking the accuracy of results is the conservation of norm of the wave function, but some other criteria might be used, such as the orthogonality of eigenfunctions and the variation of the spectrum with varying computational parameters, e.g. the number of basis functions used in the approximation. The package Spectra, which implements the spectral method in Maple language together with a number of testing tools, is presented. Alternatively, Maple may interact with the Octave numerical system without the need of Octave programming by the user. Program summary Program title: Spectral Catalogue identifier: AEQQ_v1_0 Program summaiy URL: http://cpc.cs.qub.ac.uk/summaries/AEQQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 20417 No. of bytes in distributed program, including test data, etc.: 2149904 Distribution format: tar.gz Programming language: Maple, GNU Octave 3.2.4 Computer: Any supporting Maple Operating system: Any supporting Maple RAM: About 4 Gbytes Classification: 1.9, 4.3, 4.6. Nature of problem: Numerical solution of Schrodinger-like eigenvalue equations (especially the Wheeler-DeWitt equation) in the positive semi-axis Solution method: The unknown wave function is approximated as a linear combination of a suitable set of functions, and the continuous eigenvalue problem is mapped into a discrete (matricial) eigenvalue problem Restrictions: Limitations are due to memory usage only Unusual features: The package may not work properly in older versions of Maple, due to a hug in that CAS; for that reason an interface with the GNU Octave system is provided, requiring no user intervention or Octave programming during calculations Running time: Seconds to hours, depending on the number of basis functions used and on the complexity of the potential used (C) 2013 Elsevier B.V. All rights reserved.